Question: The following line passes through point $(2, 8)$ : $y = -\dfrac{6}{7} x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(2, 8)$ into the equation gives: $8 = -\dfrac{6}{7} \cdot 2 + b$ $8 = -\dfrac{12}{7} + b$ $b = 8 + \dfrac{12}{7}$ $b = \dfrac{68}{7}$ Plugging in $\dfrac{68}{7}$ for $b$, we get $y = -\dfrac{6}{7} x + \dfrac{68}{7}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${11}$ ${12}$ ${13}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${\llap{-}11}$ ${\llap{-}12}$ ${\llap{-}13}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${11}$ ${12}$ ${13}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${\llap{-}11}$ ${\llap{-}12}$ ${\llap{-}13}$ $(2, 8)$